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Home » You Won’t Believe the Symbolism Behind Washington’s Official State Flower! - Carbonext

You Won’t Believe the Symbolism Behind Washington’s Official State Flower! - Carbonext

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 Problem:** Solve for \( x \): \( \log_2(x + 3) + \log_2(x - 1) = 3 \).

📌 Combine logs: \( \log_2((x + 3)(x - 1)) = 3 \)

📌 So \( (x + 3)(x - 1) = 2^3 = 8 \)

📌 Expand: \( x^2 + 2x - 3 = 8 \Rightarrow x^2 + 2x - 11 = 0 \)

📌 Use quadratic formula: \( x = \frac{-2 \pm \sqrt{4 + 44}}{2} = \frac{-2 \pm \sqrt{48}}{2} = \frac{-2 \pm 4\sqrt{3}}{2} = -1 \pm 2\sqrt{3} \)

📌 Since \( x > 1 \), take \( x = -1 + 2\sqrt{3} \approx -1 + 3.46 = 2.46 \), valid.

📌 #### -1 + 2√3

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